The 30-year-old is in his second spell with BVB, first playing for a couple of seasons between 2010 and 2012 before an unsuccessful stint with Manchester United.
The Japan international was back at Westfalenstadion in 2014 much to the delight of the Dortmund fans who were up in arms when he left for Old Trafford.
Kagawa had been a regular feature in the first team until the season just finished, when he fell down the pecking order following injury and was sent out on loan to Turkish giants Besiktas for the second half of the campaign.
The man with 95 Japan caps performed well, scoring four Super Lig goals from 14 outings and is now back with Dortmund.
Whether he plays for the Bundesliga side next term only time will tell as the Hammers and others are said to be interested, according to Ruhrnachrichten.de.
It has been reported that the talented schemer is unsure about his prospects with Dortmund and might look for an escape route, with both West Ham and Everton linked to the player in the past.
Manuel Pellegrini has made no secret of the fact he will bring new faces in this summer and it remains to be seen if he does his business early with the capture of Kagawa.